Conceptual design and parametric optimization of self-propelled semi-submersible repair ships: a novel equipment providing maintenance and repair support at sea

Abstract

Safety of ships and/or offshore structures at sea is increasingly crucial as seaborne activities intensify. However, maintenance and repair of them suffering marine accidents away from shipyards are an often overlooked area, with existing maintenance and/or repair ships either being of limited workshops and facilities or incapable lifting them out of water for underwater engineering. A conceptual design of a self-propelled semi-submersible repair ship is proposed for the first time to facilitate the spot maintenance and repair of damaged ships and/or offshore structures at sea, which is obviously able to reduce the time, costs and risks of transporting them from accident scenes to shipyards onshore. Furthermore, this paper focuses on parametric design and multi-objective optimization problem of this novel equipment. The ratio of deadweight to principal dimensions, working deck area and average daily cost considering marine emissions trading scheme are simultaneously chosen as objectives of this problem. Both the weighted ideal point method and the NSGA-II algorithm are used to obtain the optimization results of a 50 thousand dwt self-propelled semi-submersible repair ship and the relations and differences between the optimization results of two methods are analyzed. The research results indicate that the parametric design and multi-objective optimization method can provide theoretical support for the preliminary design.

Appendix 1: Notations and descriptions

Notations (unit)	Notation descriptions
R (ton/m3)	Ratio of deadweight to principal dimensions
S (m2)	working deck area
E (dollars/day)	Average daily cost considering METS in a voyage of carrying out MR works
DWT and ${\text{DWT}}_{0}$ (ton)	Deadweight and predetermined deadweight, respectively
L, B, D and T (m)	Length, breadth, depth and draft, respectively
$C_{{\text{B}}}$	Block coefficient
v (kn)	Sailing speed
$P_{{\text{E}}}$ (kW)	Total power
(L/B)min and (L/B)max	Lower and upper bounds of the ratio of length to breadth, respectively
(B/T)min and (B/T)max	Lower and upper bounds of the ratio of breadth to draft, respectively
(D/T)min and (D/T)max	Lower and upper bounds of the ratio of depth to draft, respectively
$C_{{\text{B}}}^{\min }$ and $C_{{\text{B}}}^{\max }$	Lower and upper bounds of block coefficient, respectively
vmin and vmax	Lower and upper bounds of sailing speed, respectively
Fn and Fnmax	Froude number [37] and its upper bound, respectively
N	Total number of conditions and $n \in \{ 1,2, \ldots ,N\}$ means the nth condition
$P_{n}$ (kW)	A required power under the nth condition
$r_{nm}$	A coefficient, 1 if the nth condition in the mth situation is required, otherwise 0
$P_{{{\text{re}}}}^{m}$ (kW)	A power that is counted twice in the mth situation
$P_{{\text{M}}}$	Shaft power
$\omega$ and $\varphi$	Parameters to calculate $P_{{\text{M}}}$
$t_{n}$ (day)	Working time under the nth condition
$\mu$	Area coefficient
$U_{{{\text{carbon}}}}$ (dollars)	Payment of carbon trading cost in a voyage based on METS
$U_{{{\text{cost}}}}$ (dollars)	Total cost except for $U_{{{\text{carbon}}}}$ in a voyage
F (dollars)	Fuel cost in a voyage
$\psi$ (dollars/ton)	Fuel price
$u$ (g/kW h)	Fuel consumption rate
H (day)	Voyage time
$\sigma$ (dollars/ton)	Price of purchasing or selling carbon emissions per unit
Q (ton)	total carbon emissions in a voyage
$\xi$ (ton/day)	average of daily carbon emission limits
$\tau$	CO2 emission coefficient of fuel
$E_{{\text{C}}}$ and $E_{{\text{I}}}$	sets of equipment in continuous and intermittent load, respectively
$P_{{\text{C}}}^{i}$ and $P_{{\text{I}}}^{j}$ (kW)	rated powers of the ith ($i \in E_{{\text{C}}}$) equipment in continuous loads and the jth ($j \in E_{{\text{I}}}$) equipment in intermittent loads, respectively
$k_{i}$ and $k_{j}$	Demand factors of the ith ($i \in E_{{\text{C}}}$) and jth ($j \in E_{{\text{I}}}$) equipment
$\lambda$	Simultaneous utilization factor
$\varepsilon$	A small amount